Flowmeter

ABSTRACT

A method and apparatus for measuring flow parameters of an unknown fluid uses four pressure sensors at fixed, spaced locations within a cylindrical member having a constricted and a full diameter portion. The constricted portion has a smooth surface of transition at its entry, internal corrugations, and a sharp increase to the full diameter at its exit. There are no moving parts. All flow parameters can be calculated from the four pressure measurements taken at the entry and exit of the constricted portion and two aligned but separated locations spaced from the sharp increase to full diameter.

BACKGROUND OF THE INVENTION

The present invention relates to a flow meter which will allowdetermination of density, flow rate, and viscosity of a conceptuallyincompressible fluid from pressure drop measurements alone.

The flow meters presently available are generally restricted to use witha particular fluid or fluid type or are limited to measuring only one ofthe three important flow parameters, namely density, flow rate andviscosity.

An example of the prior art can be found in U.S. Pat. No. 3,839,914which discloses a method and apparatus for continuously determiningdensity, velocity and Fanning friction factor, which is further used todetermine the viscosity of a liquid flowing through a closed container.The liquid is caused to flow through a conduit having a curved portionand pressure sensors are mounted on both sides of the curved portion todetermine the difference in pressure between the fluid flowing adjacentto the inside and the outside curved portion of the conduit. Furtherpressure sensors are positioned in the conduit at selected equaldistances up stream and downstream of the sensors located in the curvedportion of the conduit. The difference in pressure of the fluid betweenthese upstream and downstream locations and between the upstream anddownstream locations and the curved portion of the conduit aredetermined. These pressure determinations are then utilized in equationsto determine the desired parameters of density, flow velocity andFanning friction factor.

SUMMARY OF THE INVENTION

The present invention can be distinguished from the prior art in that itcan be used with substantially any fluid system. The density, flow rateand viscosity of a fluid can be determined from pressure measurementswhich assume no prior knowledge of the fluid. The subject flow meter canbe used at any location in a fluid system and can have any orientation.It does, however, require an incompressible, steady flow of fluid andfactoring in any angular orientation. The fluids which can be measuredwould include liquids and those gases with a velocity no more than halfthe speed of sound, provided the pressure sensing devices are capable ofmeasuring very slight pressure drops. The subject meter is an elongatedcylindrical member having a constricted section with internalcorrugations, a full width section and four pressure transducers fixedto the walls of the member at spaced locations.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described by way of example with referenceto the accompanying drawings in which:

FIG. 1 is a longitudinal section through a flow meter according to thepresent invention; and

FIG. 2 is a graph showing the friction factor relationship to theReynolds number.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

An embodiment of the present invention is shown in FIG. 1. The subjectflow meter 10 can be made either as an integral part of a longer pipesection or as a tubular member 12 which can be inserted into a largerpipe (not shown), the outer diameter of member 12 forming a close fitwith the inner diameter of the larger pipe. The subject flow meter 10has a constricted diameter section 14 (D₁) and an adjacent largerdiameter section 16 (D₂). The constricted section 14 has an entry 18which is a smooth surface of transition with a radius approximatelyequal to one-seventh of the diameter D₁ of the constricted section 14.The bore of the section 14 is formed with a continuous series ofinwardly directed corrugations 20. A first differential pressure tap Ais fixed within the entry end of the constricted section 14 while asecond differential pressure tap B is similarly fixed at the exit. Thefull diameter section 16 has a bore of a second diameter (D₂) largerthan that of the first diameter D₁. Third and fourth differentialpressure taps C and D are located in the walls of section 16 a distanceof not less than eight times the second diameter (D₂) from the interfaceof the constricted section 14 and the full diameter section 16.

The pressure taps A, B, C and D are all of any of the well known types,such as differential pressure transducers, and are fixed in the walls oftheir respective sections. Taps C and D are aligned in a transverseplane normal to the axis of the member 12 and tap D is positioned aquarter of the circumference from C so that h, the vertical spacing in ahorizontal orientation of the member, equals the radius of the fulldiameter section 16. Taps B and D are positioned to have the verticalelevation in a gravity field.

The following pressure drops are measured with the differential pressuretransducers:

ΔP_(AB)

ΔP_(BD)

ΔP_(DC)

from ΔP_(DC)

    ΔP.sub.DC =ρgh

where h=the vertical height separating the two pressure tap locations Dand C, g is gravity and ρ is density. Thus, the density can bedetermined by the equation:

    ρ=ΔP.sub.DC /gh=density

Ignoring the effects of the variation in velocity across the crosssection, which would result in a minor correction if included, we canuse ΔP_(BD), the pressure change for a sudden expansion, to obtain theflow rate. The location of the pressure taps C and D must be chosen tobe approximately eight diameters (D₂) or more downstream of the secondpressure tap B.

Considering the control volume shown in FIG. 1, the net force acting tothe right is:

    P.sub.B (πD.sub.1.sup.2 /4)+P'(π/4)(D.sub.2.sup.2 -D.sub.1.sup.2)-P.sub.D (πD.sub.2.sup.2 /4)

where P' represents the mean pressure of fluid eddies in the separatecorner regions. It has been shown that

    P'≈P.sub.B.

Thus, the net force is:

    (P.sub.B -P.sub.D)(πD.sub.2.sup.2 /4)

which equals the rate of change of momentum, where Q is the flowrate.

    (P.sub.B -P.sub.D)(πD.sub.2.sup.2 /4)=ρQ(V.sub.D -V.sub.B)

    (P.sub.B -P.sub.D)=ρV.sub.D (V.sub.D -V.sub.B)

from one energy equation ##EQU1## where h_(L) is the head loss and z isthe distance in the gravity field above a datum. Substituting for (P_(B)-P_(D)), we get ##EQU2## By continuity

    π(D.sub.1.sup.2 /4)V.sub.B =π(D.sub.2.sup.2 /4)V.sub.D

    V.sub.B =(D.sub.2.sup.2 /D.sub.1.sup.2)V.sub.D ##EQU3## The flowrate Q ##EQU4##

The density and flow rate have been determined so it is now possible todetermine the fluid viscosity. Constricted section 14 has a nominaldiameter D₁ with a sloped entrance having a radii of 1/7 the diameter D₁in order to eliminate any pressure drop due to flow contraction. Thesection is machined with regular corrugations of any desired shape andsize which will give much higher pressure drops for a given flow rate.The corrugations will also give a predictable, continuous frictionfactor-Reynolds number relationship which will be a function of therelative roughness spacing. The Reynolds number of a flow is defined asthe product of a scale velocity and a scale length divided by thekinematic viscosity of the fluid. As example is shown in the graph ofFIG. 2. This curve must be determined empirically for any given numberof corrugations, thus shape and depth.

The friction factor f is defined as ##EQU5## where L is the length ofthe conduit with a diameter D₁ over which a pressure drop ΔP ismeasured. The average velocity is V. Friction factors for corrugatedpipes will be much higher than for random spot roughness associated withcommercial pipes. Thus, a measurable pressure drop can be obtained in arelatively short section of pipe.

The viscosity of the fluid at the average or ambient temperature in thesystem may be obtained as follows: ##EQU6## from f vs Reynolds curvedetermine Re

    Re=ρ(V.sub.B D.sub.1 /μ)

    μ=ρV.sub.B D.sub.1 /Re=viscosity

To show the magnitude of pressures measured assume

D₂ =8"=20.32 cm; h=4"=10.16 cm

D₁ =4"=10.16 cm

1_(AB) =2'=2"=60.96 cm

water (at standard temperature and pressure)

μ=1×10⁻² poise=1 centipoise

ρ=1 gm/cm³ ; 1 gpm=63.08 cm³ /sec

Q=300 gpm=1.892×10⁴ cm³ /sec

    ΔP.sub.DC =ρgh=(1.0)(981)(10.16) dyn/cm.sup.2 =9.967×10.sup.3 dyn/cm.sup.2 =0.1445 psi ##EQU7## from a typical Reynolds chart f=0.1 for relative roughness spacing R/λ=3

ΔP_(AB) =(0.1)(1/2)(60.96/10.16)(1)(2.33×10²)² =1.63×10⁴ dyn/cm² =0.236psi

The pressure drops in the above example could all be measured bycommercially available differential pressure transducers. Full scalereadings can be as low as 0.08 psi and increments such as 0.125, 0.2,0.32, 0.5, 0.8 to full scale are available from a number of companies,e.g. Valedyne, Inc. For mud systems, the pressure drop should be higherthan those estimated for water and thus easier to measure.

This technique can be used with any liquid or liquid solid system.Specific systems may require special precautions in order to preventsolids settling or scale from building up and becoming a problem in thecorrugations of the constricted section and at the location of thepressure taps. If the subject meter is to be used at an angularorientation other than horizontal, then a correction for differentialpressure due to a hydrostatic component would have to be factored in.Since density is measured first, it can be used as a correction forother measurements. The subject invention is economical to fabricate andto operate since it has no moving parts.

What is claimed is:
 1. A flowmeter having no moving parts and enablingdetermination of the density, flow rate and viscosity parameters of anunknown fluid, said flowmeter comprising:an elongated cylindrical memberdefining a constricted portion of a first diameter and an adjacentdownstream full diameter portion of a second larger diameter; first andsecond pressure sensors fixed, respectively, at the entry and the exitof said constricted portion; and third and fourth pressure sensors fixedin said full diameter portion at a distance of at least eight times thesecond diameter from the junction of said constricted and said fulldiameter portions, wherein said fourth pressure sensor is aligned withsaid third pressure sensor in a plane extending normal to the axis ofsaid meter whereby differential pressure readings can be obtained andused to determine the density, flow rate and viscosity of a fluidpassing therethrough.
 2. The flowmeter according to claim 1 wherein saidconstricted portion has a smooth surface of transition of a radiusone-seventh of the first diameter forming an entry whereby pressurechange due to flow contraction is minimized.
 3. The flowmeter accordingto claim 1 wherein said constricted portion has an internal surfaceformed by a series of corrugations.
 4. The flowmeter according to claim1 wherein said fourth pressure sensor is spaced from said third pressuresensor such that the vertical spacing between them equals the radius ofsaid second diameter.
 5. The flowmeter according to claim 1 wherein saidfourth pressure sensor is spaced from said second pressure sensorone-quarter of the circumference of the full diameter portion.
 6. Theflowmeter according to claim 1 wherein said second and fourth pressuresensors have the same vertical elevation in a field of gravity.
 7. Theflowmeter according to claim 1 wherein said elongated cylindrical memberis integrally formed with a longer section of pipe.
 8. The flowmeteraccording to claim 1 wherein said elongated cylindrical member has anouter diameter allowing said flowmeter to be received with close fitwithin a larger diameter pipe.
 9. The flowmeter according to claim 1wherein said elongated cylindrical member is integral.
 10. The flowmeteraccording to claim 1 wherein said pressure sensors are differentialpressure transducers.
 11. A method for determining the density, flowrate and viscosity parameters of a fluid comprising the steps of:flowingthe fluid through a conduit having a constricted portion of a firstdiameter (D₁) and a full width portion of a larger second diameter (D₂);determining the pressure of the fluid at a first point at the entry ofsaid constricted portion; determining the pressure of the fluid at asecond point at the exit of said constricted portion; determining thepressure of the fluid at a third point in said full width portion spacedfrom the exit of said constricted portion; determining the pressure ofthe fluid at a fourth point spaced above and aligned with the thirdpoint; and determining the density, flow rate and viscosity,respectively, in accordance with the following equations:

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points, ##EQU8## where ΔP_(BD) is the pressuredifferential between the second and fourth points,

    μ=ρV.sub.B D.sub.1 /Re

where Re is the Reynolds number and V_(B) is average velocity from theequation ##EQU9##
 12. A method for determining the density of a fluidcomprising the steps of:flowing the fluid through a conduit having aconstricted portion of a first diameter (D₁) and a full width portion ofa larger second diameter (D₂); determining the pressure of the fluid ata first point at the entry of said constricted portion; determining thepressure of the fluid at a second point at the exit of said constrictedportion; determining the pressure of the fluid at a third point in saidfull width portion spaced from the exit of said constricted portion;determining the pressure of the fluid at a fourth point spaced above andaligned with the third point; and determining the density in accordancewith the equation

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points.
 13. A method for determining the flow rate of afluid comprising the steps of:flowing the fluid through a conduit havinga constricted portion of a first diameter (D₁) and a full width portionof a larger second diameter (D₂); determining the pressure of the fluidat a first point at the entry of said constricted portion; determiningthe pressure of the fluid at a second point at the exit of saidconstricted portion; determining the pressure of the fluid at a thirdpoint in said full width portion spaced from the exit of saidconstricted portion; determining the pressure of the fluid at a fourthpoint spaced above and aligned with the third point; and determining theflow rate in accordance with the following equation: ##EQU10## whereΔP_(BD) is the pressure differential between the second and fourthpoints and ρ is the density of the fluid.
 14. The method according toclaim 13 wherein the density is determined in accordance with theequation

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points.
 15. A method for determining the viscosity of afluid comprising the steps of:flowing the fluid through a conduit havinga constricted portion of a first diameter (D₁) and a full width portionof a larger second diameter (D₂); determining the pressure of the fluidat a first point at the entry of said constricted portion; determiningthe pressure of the fluid at a second point at the exit of saidconstricted portion; determining the pressure of the fluid at a thirdpoint in said full width portion spaced from the exit of saidconstricted portion; determining the pressure of the fluid at a fourthpoint spaced above and aligned with the third point; and utilizing theabove pressures for determining the viscosity in accordance with thefollowing equation:

    μ=ρV.sub.B D.sub.1 /Re

where Re is the Reynolds number and V_(B) the average velocity in theconstricted portion.
 16. The method according to claim 15 wherein saidvelocity is determined from the equation ##EQU11## where ρ is thedensity of the fluid and ΔP_(BD) is the pressure differential betweenthe second and fourth points.
 17. The method according to claim 16wherein said density is determined from the equation

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points.
 18. A method for determining the density andflow rate of a fluid comprising the steps of:flowing the fluid through aconduit having a constricted portion of a first diameter (D₁) and a fullwidth portion of a larger second diameter (D₂); determining the pressureof the fluid at a first point at the entry of said constricted portion;determining the pressure of the fluid at a second point at the exit ofsaid constricted portion; determining the pressure of the fluid at athird point in said full width portion spaced from the exit of saidconstricted portion; determining the pressure of the fluid at a fourthpoint spaced above and aligned with the third point; and determining thedensity and flow rate in accordance with the following equations:

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points, ##EQU12## where ΔP_(BD) is the pressuredifferential between the second and fourth points.
 19. A method fordetermining the flow rate and viscosity of a fluid comprising the stepsof:flowing the fluid through a conduit having a constricted portion of afirst diameter (D₁) and a full width portion of a larger second diameter(D₂); determining the pressure of the fluid at a first point at theentry of said constricted portion; determining the pressure of the fluidat a second point at the exit of said constricted portion; determiningthe pressure of the fluid at a third point in said full width portionspaced from the exit of said constricted portion; determining thepressure of the fluid at a fourth point spaced above and aligned withthe third point; and determining the flow rate and viscosity,respectively, in accordance with the following equations: ##EQU13##where ΔP_(BD) is the pressure differential between the second and fourthpoints, and ρ is the fluid density,

    μ=ρV.sub.B D.sub.1 /Re

where Re is the Reynolds number and V_(B) is average velocity from theequation ##EQU14##
 20. A method according to claim 19 wherein saiddensity is determined by the equation:

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points.
 21. A method for determining the density andviscosity parameters of a fluid comprising the steps of:flowing thefluid through a conduit having a constricted portion of a first diameter(D₁) and a full width portion of a larger second diameter (D₂);determining the pressure of the fluid at a first point at the entry ofsaid constricted portion; determining the pressure of the fluid at asecond point at the exit of said constricted portion; determining thepressure of the fluid at a third point in said full width portion spacedfrom the exit of said constricted portion; determining the pressure ofthe fluid at a fourth point spaced above and aligned with the thirdpoint; and determining the density and viscosity, respectively, inaccordance with the following equations:

    ρ=ΔP.sub.DC /gh

where ΔP_(DC) is the pressure differential between said third and saidfourth points, g is gravity, and h is the vertical spacing between thethird and fourth points,

    μ=ρV.sub.B D.sub.1 /Re

where Re is the Reynolds number, V_(B) is average velocity from theequation ##EQU15## and ΔP_(BD) is the pressure differential between thesecond and fourth points.